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P. Giommi
ESIS, Information Systems Division, ESA/ESRIN, Frascati, Italy
N. E. White, L. Angelini
HEASARC, NASA/GSFC, Greenbelt, MD 20771
Systematic studies of luminosity variability in data obtained from low orbit satellites often require binning and are complicated by the frequent data interruptions due to Earth occultation and other causes. We present here a method to detect X-ray variations that does not require binning, is simple, and numerically stable, and is not sensitive to data interruptions. Variability on time scales ranging from a few seconds to the actual observation duration can be detected. We have used this technique to systematically analyze of all PSPC images available in the ROSAT public archive. This project led to the construction of a catalog including more than 40,000 X-ray sources (the WGA catalog, White, Giommi, and Angelini 1994). Several hundred of these sources have been found to be rapidly variable.
The method consists in comparing the time arrival distribution of the
photons collected in each pixel with the corresponding distribution of
the entire image using a Kolmogorov-Smirnov (KS) test. The result of the KS
test is a 
value (with 2 degrees of freedom) that is used to assign an
intensity value to each pixel. In this way, pixels where
the distribution of photon arrival times is not consistent with that of the
entire image are given high intensity (
) values.
The time variability image so constructed visually shows
area where strong time variation occurred.
To calculate the 
values the event list must be time sorted
and must be read twice.
The first time the event list is read a normal intensity image is
built and is stored in memory as an array of integers.
This array is used during the second pass to provide the normalization
values (i.e., the number of detected photons during the
full exposure) in each pixel and in the entire image.
The second time the event list is read, the cumulative distributions
for each pixel and for the entire image are calculated.
When a photon i is considered the cumulative distribution at time
in pixel
(
) is obtained as the
ratio of the number of photons detected up to time 
divided by the total number of photons detected at position (
):
.
The cumulative distribution of the whole image is calculated as the
ratio of all the photons arrived up to time 
, and the total number of
photons in the image accumulated during the entire exposure is
. The distance 
between the two distributions is written into
a new array at location (
) only if it is greater than the
value previously stored in that pixel. These steps are repeated for
every photon in the event list. At the end of this process the array containing the
(maximum) distances between the arrival time distribution of all pixels
and the entire image is converted into an array of 
values using
the usual formula of the KS test.
This method has been incorporated within the XIMAGE package (Giommi et al.
1991). In this particular implementation the KS test is
applied only to pixels where more than 10 photons were detected during
the entire observation. The resulting 
values are multiplied by a factor 10, to increase the dynamic range, and
are limited to a maximum value of 200 to avoid that a bright variable
source with a very high 
dominating the entire image. By this method,
all pixels with values between 
100 and 200 represent variable
sources.
The method is based on the comparison between the source light curve and that of the rest of the image. To properly detect source variations it is necessary that the image background be not strongly variable. This condition is generally satisfied in most ROSAT images. For the case of observations with highly variable background it is necessary to remove all the time intervals where the background was variable. This obviously reduces the sensitivity of the test. A second limitation of this method is that it is not sensitive to small amplitude variability (less than about a factor 2) and to weak periodic oscillations.
Given the limitations described, this method cannot be used to perform uniform variability surveys. It is, however, very useful for detecting large flares (on time scales of hours or days) or strong periodic sources. In all cases a careful check must be carried out to remove spurious events. This is an ongoing activity on the candidate variable sources included in the WGA catalog.
In this section we give some examples of rapidly variable sources found in ROSAT public data using the ESIS system (Giommi et al. 1994) which makes use of XIMAGE and several other Xanadu routines. Figure 1. shows the intensity (left) and time variability (right) image of the ROSAT field centered on the X-ray source MKW 3. A strongly variable source is clearly visible in the bottom-right part of the right image; its light curve is shown in Figure 2. Figure 3 shows a PSPC exposure of the Orion region where several sources have been detected (left). The corresponding time variability image is shown to the right. At least three sources varied during the observation. The light curves of two of these variable sources are shown in Figure 4. These examples clearly show the power of the method described in evidencing variable sources in crowded X-ray images.
Figure: Intensity and time variability image of the ROSAT field
centered on MKW 3.
Original PostScript figure (411 kB)
Figure: The light curve of the variable source shown in Figure 1.
Original PostScript figure (1089 kB)
Figure: Intensity and time variability image of a ROSAT field
in the Orion region.
Original PostScript figure (1242 kB)
Figure: The light curves of the top left (upper panel) and middle
left (lower panel) variable sources of Figure 3.
Original PostScript figure (1056 kB)
Giommi, P., Ansari, S. G., Donzelli, P., & Micol, A. 1994, Experimental Astronomy, in press
Giommi, P., Angelini, L., Jacobs P., & Tagliaferri, G. 1991, in Astronomical Data Analysis Software and Systems I, ASP Conf. Ser., Vol. 25, eds. D.M. Worrall, C. Biemesderfer, & J. Barnes (San Francisco, ASP), p. 100
White, N. E., Giommi, P., & Angelini, L. 1994, Proceedings of the AAS-HED meeting, The Multi-Mission Perspective (Napa Valley, AAS-HED)
3784 kB PostScript reprint